Semiparametric Double Balancing Score Estimation for Incomplete Data With Ignorable Missingness

When estimating the marginal mean response with missing observations, a critical issue is robustness to model misspecification. In this article, we propose a semiparametric estimation method with extended double robustness that attains the optimal efficiency under less stringent requirement for model specifications than the doubly robust estimators. In this semiparametric estimation, covariate information is collapsed into a two-dimensional score S , with one dimension for (i) the pattern of missingness and the other for (ii) the pattern of response, both estimated from some working parametric models. The mean response E ( Y ) is then estimated by the sample mean of E ( Y ∣ S ), which is estimated via nonparametric regression. The semiparametric estimator is consistent if either the “core” of (i) or the “core” of (ii) is captured by S , and attains the optimal efficiency if both are captured by S . As the “cores” can be obtained without correctly specifying the full parametric models for (i) or (ii), the proposed estimator can be more robust than other doubly robust estimators. As S contains the propensity score as one component, the proposed estimator avoids the use and the shortcomings of inverse propensity weighting. This semiparametric estimator is most appealing for high-dimensional covariates, where fully correct model specification is challenging and nonparametric estimation is not feasible due to the problem of dimensionality. Numerical performance is investigated by simulation studies.